This invention relates generally to plasma devices and particularly to the confinement and stabilization of plasmas in fusion devices of the reversed field pinch (RFP) and related classes, the confining magnetic fields of which are generated primarily by axially directed electric current and which are stabilized principally by reversal of the magnetic field line pitch and by magnetic shear. More particularly, the present invention relates to the generation of a large translational transform by shaping of the plasma cross section as a means of aiding pitch reversal and increasing magnetic shear. The invention is operative with both open ended, topologically linear plasmas, and with closed, topologically toroidal plasmas. A topological torus is any geometric solid figure that can be produced by an imagined elastic deformation of an initial circular torus.
The problems in nuclear fusion devices are largely to heat the plasma to a high enough temperature to enable the desired reactions to occur and to confine the heated plasma for a time long enough to release energy in excess of that required to heat the plasma to reaction temperature. The present invention is directed to the magnetic confinement of such plasma and finds particular utility in such devices and their applications, including experimental devices and the use thereof in experimentation and investigation with respect to plasma devices. Toroidal plasma devices are the most effective in the confinement of the high temperature plasmas of fusion interest. Toroidal plasma devices are devices in which plasma is created in a topologically toroidal space and is confined therein by appropriate magnetic fields.
The magnetohydrodynamic (MHD) stability of a magnetically confined plasma is dependent on the pitch of the magnetic field lines encircling a magnetic axis. This pitch P is defined by ##EQU1## where .DELTA..zeta. is the distance a field line advances along the direction of the magnetic axis and k the number of times the axis is encircled. This limit is the same for all possible field lines on a given magnetic surface. A magnetic surface is defined as a mathematical surface on which the magnetic field has no component normal thereto. The magnetic surface enclosing zero volume in the center of nested magnetic surfaces is called an elliptic magnetic axis, or simply the magnetic axis when there is no other kind of magnetic axis. The magnetic shear s can be defined and is defined herein, as ##EQU2## where r is any convenient monotonic variable (for example, an average radius) that labels the distance of the magnetic surfaces from the magnetic axis. Some minimal conditions of MHD stability are:
1. s.noteq.O, except at the magnetic axis.
2. .vertline.q.vertline..noteq.1, q being the so-called safety factor defined by q.ident.2.pi.P/L, where L is the length of the magnetic axis, i.e., in the case of a toroidal configuration, the length around the torus along the magnetic axis, and in the case of a linear configuration, the length from end to end along the magnetic axis.
3. .vertline.s.vertline. is sufficiently large to satisfy the Mercier criterion. C. Mercier, "Critere de Stabilite d'an Systeme Toroidal Hydromagnetique en Pression Scalaire," Nuclear Fusion Supp., Part 2, pp. 801-808 (1962).
A pinch effect takes place when large e1ectric current flowing through the plasma is acted upon by its own magnetic field to exert a confining pressure on the plasma. The large current simultaneously heats the plasma ohmically. The simplest pinch configuration, called the Bennett pinch, is unstable, and most of the plasma soon strikes the confinement vessel, hence cooling the plasma and impeding any reaction. Therefore, the simple pinch must be modified to improve its stability. The most successful pinch for magnetic confinement of plasmas to date has been the reversed field pinch.
A review of the RFP art was given by H. A. B. Bodin and A. A. Newton, "Reversed-Field-Pinch Research," Nucl. Fusion 20, pp. 1255-1324 (1980). The RFP is a diffuse z-pinch of circular cross section in which the magnetic field component sensibly parallel to the magnetic axis has a direction in the outside region of the plasma opposite to that in the inner region, and as a result, P(r) passes through zero and changes sign within the plasma, where r is the minor radius measured from the magnetic axis. As discussed in the Bodin and Newton publication in conjunction with FIG. 7 thereof, the reversal of P within the plasma is necessary to ensure monotonicity of P through the transition region between the plasma and the surrounding vacuum. In actual experiments with conventional RFPs, the level of instability is notably reduced once the reversed pitch profile is established. Because of increasingly successful experiments, the reversed field pinch principle is of growing interest for the achievement of fusion energy. However, stabilization is not complete in the RFP, and this may be the cause of reduced plasma confinement when compared with other confinement devices, such as tokamaks. It is commonly accepted that the azimuthal plasma current needed to maintain the desired reversed axial magnetic field, which current cannot be sustained by means external to the plasma, is driven by an as yet unidentified "plasma dynamo" mechanism linked to low level plasma instability.
A more global theory of the stability of the RFP and related pinch plasmas was advanced in J. B. Taylor, "Relaxation of Toroidal Plasma and Generation of Reverse Magnetic Fields," Physical Review Letters 33, pp. 1139-1141 (1974), which showed that the minimum energy, and hence most stable, state accessible to a plasma that conserves global magnetic helicity must obey the equation EQU .gradient..times.B=.mu.B, (3)
where B is the magnetic flux density or field and .mu. is a constant. Equation 3 describes a Taylor state plasma. It can also be written as EQU .mu..sub.o j=.mu.B, (4)
where j is the electric current density and .mu..sub.o is the magnetic permeability of free space. Actual RFP plasma fields approximate Equations (3) and (4) rather well. The principal discrepancy is that .mu. is not a constant but drops to zero or a small value near the edge of the plasma which reduces the magnetic shear and plasma stability there. However, it is known from detailed results of conventional MHD stability theory that a gradient in .mu. is a destabilizing factor. Because plasma near the edge is cold and poorly conducting, a reduction in j, and hence the gradient in .mu. near the edge, appears inevitable. It would be desirable to augment the magnetic shear in this region to reduce, and perhaps overcome, the destabilizing effect. It would also be desirable to reduce the magnitude of the azimuthal current in the plasma needed to maintain a pitch-reversed configuration. This is desirable because azimuthal current is driven by the plasma dynamo, which depends upon turbulence in the plasma, but turbulence leads to loss of plasma, and because the plasma dynamo effect is self-regulating, whereby by requiring less plasma dynamo for producing azimuthal current there is less plasma loss. According to the present invention, increased magnetic shear and decreased azimuthal current may be achieved by adding a large translational transform to augment the pitch reversal.
Translational transform is shown by T. Ohkawa, U.S. Pat. No. 4,302,284. It consists of changing the direction of an otherwise azimuthally directed magnetic field (around the magnetic axis), such as predominates in z-pinches, to have a mean axial component (in the direction of the magnetic axis) as well, by giving the plasma a helically symmetric shape by means of external electrical conductors. The Ohkawa device utilizes multipolar helical windings for this purpose. However, the practical amount of change obtainable by this method, which relies on proximity of the plasma to a magnetic separatrix, appears to be inherently limited to less than about 10.degree., and the transform is localized near the separatrix. It is an aspect of the present invention to produce a much larger translational transform for an RFP-like plasma.